11. P.H. Gudiksen, A.W. Fairhall, and R.J. Reed. Roles of Mean Meridional Circulation and Eddy Diffusion in the Transport of Trace Substances in the Lower Stratosphere, J. Geophys. Res. 73, 4461-4473, 1968. 12. F.M. Luther, Large-scale Eddy Diffusion, CIAP Monograph 1, The Natural Stratosphere of 1974, Department of Transportation Report DOT-TST-75-51, 1975. 13. E. Bauer. Dispersion of Tracers in the Atmosphere and Ocean: Survey and Comparison of Experimental Data, J. Geophys. Res. 79, 789-795, 1974. 14. A. Ebel, Eddy Diffusion Models for the Mesosphere and Lower Thermosphere, J. Atmos. Terr. Phys. 42, 617-628, 1980. 15. W.J. Borucki, R.C. Whitten. H.T. Woodward. L.A. Capone, C.A. Riegel, and S. Gaines, Stratospheric Ozone Decrease Due to Chlorofluoromethane Photolysis: Predictions of Latitude Dependence, JAS 37, 686-697, 1980. 16. R.C. Whitten, W.J. Borucki, V.R. Watson, T. Shimazaki, H.T. Woodward, C.A. Riegel, L.A. Capone, and T. Becker, The NASA Ames Research Center One- and Two-Dimensional Stratospheric Models. II: The Two-Dimensional Model, NASA TP-1003, 1977. 17. J.D. Mahlman, Some Fundamental Limitations of Simplified Transport Models as Implied by Results From a Three-Dimensional General Circulator/Tracer Model, Proceedings Fourth Conference on CIAP, DOT-TSC-OST-75-38, pp. 132-146, 1975. 18. E.F. Danielsen and J. Louis, Transport in the Stratosphere, in The Upper Atmosphere and Magnetosphere, National Academy of Sciences, Washington, DC, 1977. 19. ESSA Technical Report WV 12, Weekly Synoptic Analyses, 5-, 2-, and 0.4-Millibar Surfaces for 1967, U.S. Department of Commerce, 1970. APPENDIX A. DERIVATION OF THE MERIDIONAL LENGTH SCALE, L In the diffusion approximation, the equation representing the transport of trace constituents with a mixing fraction, </>, can be expressed as for an isothermal atmosphere with scale height H. In Eq. Al, Km and Kzz are the horizontal and vertical eddy diffusivities, respectively; pt is the sine of the latitude; J is the net chemical loss rate (negligibly small for water vapor); q0 is the source strength at coordinates Qx', z'); and the 8 values are delta functions. Except at high latitudes, the first term on the left-hand side can be approximated by (K^/R^d^/dO2), where 0 is the latitude. Applying the convenient condition d<f>ldz = at the upper boundary (located at z = z„, about 17 scale heights above the lower boundary), <6 = 0 at the lower boundary (z = 0), and vanishing fluxes across the poles, leads to which comes from the denominator in Eq. A2 when n = 1, m = 1; that is, only the first term in expansion A2 contributes significantly, and the higher-order terms nearly cancel. For values Kvu ~ 2 x 106 m2/s and Kzz ~ 30 m2/s (typical for our two-dimensional model) and // = 6 km, we estimate that L ~ 3000 km, a value in good agreement with the numerical model results and the results obtained from a term-by-term expansion of Eq. A2 up to n,m = 10.
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